Low-Temperature Non-Ohmic Galvanomagnetic Effects in Degeneraten-Type InAs

Abstract

The dependence of the mobility of $n$-InAs on temperature and electric field was measured between 4.2 and 30 K and 0.05 and 10 V/cm, respectively. Furthermore, the variation of the nonoscillatory as well as the oscillatory part of the magnetoresistance (Shubnikov-de Haas effect) with applied electric field was studied experimentally. It was found that the decrease of the amplitudes of the Shubnikov-de Haas (SdH) effect depends on the time after application of the electric field and allows a direct time-resolved observation of the increasing electron temperature. The non-Ohmic transport is interpreted with the aid of an electron-temperature model. At electric fields below 0.3 V/cm, where the electron gas is strongly degenerate, electron temperatures are deduced from the decreases of the SdH amplitudes. At higher fields the degeneracy decreases gradually and electron temperatures are obtained from a comparison of the field-dependent non-Ohmic mobility and the temperature-dependent Ohmic mobility. From energy-balance considerations, the dependences of the electron temperature and the mobility on the electric field strength are calculated up to 10 V/cm assuming that ionized-impurity scattering is the dominant mechanism for momentum relaxation. The energy loss was assumed to involve scattering by acoustic phonons via the screened deformation potential and the screened piezoelectric interaction, and also scattering by polar optical phonons. A value of 4.05 eV for the deformation potential constant yielded good agreement between the experimental and the calculated dependence of the energy-loss rate on the electron temperature up to 18 K. Above 18 K the energy loss because of polar optical phonons, which is çalculated for a degenerate electron gas, dominates the increase of the electron temperature and leads to a kink in the mobility-field characteristic. The nonoscillatory positive magnetoresistance is shown to be dependent on the electric field. The negative magnetoresistance of the samples under investigation was studied between 2.4 and 4.2 K. A semiempirical relation of the form $\frac{\Delta \rho }{{\rho }_0}=-B_1 \ln [1+B_2\mathrm{}(T\left)\mathrm{}{B}^2\right]$ was used to analyze the data.